I’d like to start by saying that the answer to this question is going to differ from person to person. It’s asking an opinion. Different people are going to find different stories more relevant. What’s more important than the story choice is the support given for why you believe that...
story is most relevant today.
For me, I would choose “The Cask of Amontillado.” At its core, the story is a story of revenge. Fortunato offends Montresor in some way, and Montresor vows revenge. Montresor then deviously puts his revenge plans in motion, and they end with the destruction (death) of Fortunato.
The reason that I believe this story is relevant today is because I see that same revenge theme in a lot of media. ABC even has a show titled Revenge. I feel that the revenge motif as a tool to drive a plot forward is incredibly common now. I find it disturbing as well because I believe that readers and viewers might begin to see the concept of revenge as normal. That normality is another reason why I think the story is applicable to a modern audience. Montresor doesn’t hesitate with his plan, nor does he feel guilty or remorseful about his actions. He feels entirely justified in killing Fortunato over some unknown insult. Revenge seems like a normal concept for Montresor.
However, even though “The Cask of Amontillado” uses revenge to drive the plot forward, I feel that the story is distinctly different than modern-day media examples of revenge. I feel that the story is different because in most modern media examples that focus on revenge, the person going about getting revenge is painted as the “good guy” hero. I’ll give a classic example. Inigo Montoya from The Princess Bride has vowed revenge against the six-fingered man for killing his father. Audiences root for Montoya throughout the film and cheer for him when he finally kills his foe. It’s the same when Maximus Decimus Meridius from Gladiator vows revenge against Commodus. Audiences are perfectly fine with Maximus leaving a huge body count in his wake because it’s in the name of revenge. It’s different in “The Cask of Amontillado,” though. Montresor might be the main character, but readers don’t find themselves rooting for him. We should be (and are) appalled at the murder that he commits. We see him as a bad guy doing morally destitute things, and the fact that he has no guilt about it makes him even more evil.
I think that this story is incredibly relevant to modern audiences because I believe it shows revenge as something that a person shouldn’t aspire to taking. The story is quite dark in its content, but I feel that it is a refreshing look at a common motif. It doesn’t show revenge in a positive light.